List of practice Questions

Let f : R $/to$ R be given by f(x) = (x - 1)(x - 2)(x - 5). Define $F\left(x\right) = \int\limits^{x}_{0} f\left(t\right) dt, x > 0.$ Then which of the following options is/are correct?

A carnot engine takes 300 calories of heat at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

Which of the following is not permissible arrangement of electrons in an atom.

If det $\begin{bmatrix}1&1&2\\ 2&4&9\\ t&t^{2}&1+t^{3}\end{bmatrix} = 0 $ , then the values of t are

Which one of the following properties has same value for $H_2$ and $D_2$ ?

Induction furnace uses ______ to produce heat

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is:

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

\[\log(\sin 1^\circ) \times \log(\sin 2^\circ) \times \ldots \times \log(\sin 90^\circ) \text{ is}\]

The probability that a leap year will have 53 Fridays or 53 Saturday is

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 sec, yellow for 5 sec and red for 30 sec. At a randomly chosen time, the probability that the light will not be green is

Which one of the following is a mineral of iron?

E° for the cell, \(Zn|Zn^{2+} (aq) ||Cu^{2+} (aq)|Cu(s)\) is 1.01 V at 25°C. The equilibrium constant for the cell reaction \(Zn + Cu^{2+} (aq) ⇋ Cu+ Zn^{2+} (aq)\) is of the order of

Reagent used to convert allyl alcohol to acrolein is

Which of the following colligative properties can provide molar mass of proteins (or polymers or colloids) with greatest precision?

Which of the following is a bactericidal antibiotic ?

In what manner will increase of pressure affect the following equation ?
\(C(s)+H_2O(g)⇋CO(g)+H_2(g)\)

The radius of a calcium ion is 94 pm and of the oxide ion is 146 pm. The possible crystal structure of calcium oxide will be

What is order with respect to A, B, C respectively?

[A]	[B]	[C]	Rate (M/sec.)
0.2	0.1	0.02	8.08 × 10-3
0.1	0.2	0.02	2.01 × 10-3
0.1	1.8	0.18	6.03 × 10-3
0.2	0.1	0.08	6.464 × 10-2

Which of the following act as epimeric pair?

Which of the following rare gas is the abundant in air?

A mass falls from a height 'h' and its time of fall $'l'$ is recorded in terms of time period T of a simple pendulum. On the surface of earth it is found that I = 2T. The entire set up is taken on the surface of another planet whose mass is half of that of earth and radius the same. Same experiment is repeated and corresponding times noted as t' and T'.